[2506.08618] HSG-12M: A Large-Scale Benchmark of Spatial Multigraphs from the Energy Spectra of Non-Hermitian Crystals

Computer Science > Machine Learning arXiv:2506.08618 (cs) [Submitted on 10 Jun 2025 (v1), last revised 5 Mar 2026 (this version, v3)] Title:HSG-12M: A Large-Scale Benchmark of Spatial Multigraphs from the Energy Spectra of Non-Hermitian Crystals Authors:Xianquan Yan, Hakan Akgün, Kenji Kawaguchi, N. Duane Loh, Ching Hua Lee View a PDF of the paper titled HSG-12M: A Large-Scale Benchmark of Spatial Multigraphs from the Energy Spectra of Non-Hermitian Crystals, by Xianquan Yan and 4 other authors View PDF HTML (experimental) Abstract:AI is transforming scientific research by revealing new ways to understand complex physical systems, but its impact remains constrained by the lack of large, high-quality domain-specific datasets. A rich, largely untapped resource lies in non-Hermitian quantum physics, where the energy spectra of crystals form intricate geometries on the complex plane -- termed as Hamiltonian spectral graphs. Despite their significance as fingerprints for electronic behavior, their systematic study has been intractable due to the reliance on manual extraction. To unlock this potential, we introduce Poly2Graph: a high-performance, open-source pipeline that automates the mapping of 1-D crystal Hamiltonians to spectral graphs. Using this tool, we present HSG-12M: a dataset containing 11.6 million static and 5.1 million dynamic Hamiltonian spectral graphs across 1401 characteristic-polynomial classes, distilled from 177 TB of spectral potential data. Crucially, HSG-...